Two classes of optimal ternary cyclic codes with minimum distance four

Abstract

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let C(t,e) denote the cyclic code with two nonzero αt and αe, where α is a generator of 𝔽*3m. In this letter, we investigate the ternary cyclic codes with parameters [3m-1, 3m-1-2m, 4] based on some results proposed by Ding and Helleseth in 2013. Two new classes of optimal ternary cyclic codes C(t,e) are presented by choosing the proper t and e and determining the solutions of certain equations over 𝔽3m.